Dell 1815dn constantly shows as "offline" - Win7

I have a Dell MFP 1815dn and am running Win 7 64 bit, but I had the same problem with this printer on XP. This is a networked printer, so both the desktop and 2 laptops use it. The printer frequently shows as "offline" on the laptops and will not print. Nothing we can do seems to reset it -- we end up rebooting both devices several times until it finally works or, if that does not work, uninstalling and reinstalling the driver. Obviously that is not a workable solution.

I can't find anything on this problem -- what does "offline" mean, and how can I get it to stop going offline, and how can I get it back "online" when it does?